mirror of
https://github.com/titanscouting/tra-analysis.git
synced 2024-12-26 17:49:09 +00:00
907 lines
31 KiB
Python
907 lines
31 KiB
Python
from __future__ import absolute_import
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from itertools import chain
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import math
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from six import iteritems
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from six.moves import map, range, zip
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from six import iterkeys
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import copy
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try:
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from numbers import Number
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except ImportError:
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Number = (int, long, float, complex)
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inf = float('inf')
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class Gaussian(object):
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#: Precision, the inverse of the variance.
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pi = 0
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#: Precision adjusted mean, the precision multiplied by the mean.
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tau = 0
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def __init__(self, mu=None, sigma=None, pi=0, tau=0):
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if mu is not None:
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if sigma is None:
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raise TypeError('sigma argument is needed')
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elif sigma == 0:
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raise ValueError('sigma**2 should be greater than 0')
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pi = sigma ** -2
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tau = pi * mu
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self.pi = pi
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self.tau = tau
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@property
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def mu(self):
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return self.pi and self.tau / self.pi
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@property
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def sigma(self):
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return math.sqrt(1 / self.pi) if self.pi else inf
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def __mul__(self, other):
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pi, tau = self.pi + other.pi, self.tau + other.tau
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return Gaussian(pi=pi, tau=tau)
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def __truediv__(self, other):
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pi, tau = self.pi - other.pi, self.tau - other.tau
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return Gaussian(pi=pi, tau=tau)
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__div__ = __truediv__ # for Python 2
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def __eq__(self, other):
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return self.pi == other.pi and self.tau == other.tau
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def __lt__(self, other):
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return self.mu < other.mu
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def __le__(self, other):
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return self.mu <= other.mu
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def __gt__(self, other):
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return self.mu > other.mu
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def __ge__(self, other):
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return self.mu >= other.mu
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def __repr__(self):
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return 'N(mu={:.3f}, sigma={:.3f})'.format(self.mu, self.sigma)
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def _repr_latex_(self):
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latex = r'\mathcal{{ N }}( {:.3f}, {:.3f}^2 )'.format(self.mu, self.sigma)
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return '$%s$' % latex
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class Matrix(list):
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def __init__(self, src, height=None, width=None):
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if callable(src):
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f, src = src, {}
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size = [height, width]
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if not height:
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def set_height(height):
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size[0] = height
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size[0] = set_height
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if not width:
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def set_width(width):
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size[1] = width
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size[1] = set_width
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try:
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for (r, c), val in f(*size):
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src[r, c] = val
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except TypeError:
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raise TypeError('A callable src must return an interable '
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'which generates a tuple containing '
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'coordinate and value')
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height, width = tuple(size)
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if height is None or width is None:
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raise TypeError('A callable src must call set_height and '
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'set_width if the size is non-deterministic')
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if isinstance(src, list):
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is_number = lambda x: isinstance(x, Number)
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unique_col_sizes = set(map(len, src))
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everything_are_number = filter(is_number, sum(src, []))
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if len(unique_col_sizes) != 1 or not everything_are_number:
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raise ValueError('src must be a rectangular array of numbers')
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two_dimensional_array = src
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elif isinstance(src, dict):
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if not height or not width:
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w = h = 0
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for r, c in iterkeys(src):
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if not height:
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h = max(h, r + 1)
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if not width:
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w = max(w, c + 1)
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if not height:
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height = h
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if not width:
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width = w
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two_dimensional_array = []
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for r in range(height):
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row = []
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two_dimensional_array.append(row)
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for c in range(width):
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row.append(src.get((r, c), 0))
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else:
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raise TypeError('src must be a list or dict or callable')
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super(Matrix, self).__init__(two_dimensional_array)
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@property
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def height(self):
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return len(self)
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@property
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def width(self):
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return len(self[0])
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def transpose(self):
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height, width = self.height, self.width
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src = {}
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for c in range(width):
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for r in range(height):
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src[c, r] = self[r][c]
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return type(self)(src, height=width, width=height)
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def minor(self, row_n, col_n):
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height, width = self.height, self.width
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if not (0 <= row_n < height):
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raise ValueError('row_n should be between 0 and %d' % height)
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elif not (0 <= col_n < width):
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raise ValueError('col_n should be between 0 and %d' % width)
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two_dimensional_array = []
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for r in range(height):
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if r == row_n:
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continue
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row = []
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two_dimensional_array.append(row)
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for c in range(width):
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if c == col_n:
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continue
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row.append(self[r][c])
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return type(self)(two_dimensional_array)
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def determinant(self):
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height, width = self.height, self.width
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if height != width:
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raise ValueError('Only square matrix can calculate a determinant')
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tmp, rv = copy.deepcopy(self), 1.
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for c in range(width - 1, 0, -1):
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pivot, r = max((abs(tmp[r][c]), r) for r in range(c + 1))
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pivot = tmp[r][c]
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if not pivot:
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return 0.
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tmp[r], tmp[c] = tmp[c], tmp[r]
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if r != c:
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rv = -rv
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rv *= pivot
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fact = -1. / pivot
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for r in range(c):
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f = fact * tmp[r][c]
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for x in range(c):
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tmp[r][x] += f * tmp[c][x]
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return rv * tmp[0][0]
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def adjugate(self):
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height, width = self.height, self.width
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if height != width:
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raise ValueError('Only square matrix can be adjugated')
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if height == 2:
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a, b = self[0][0], self[0][1]
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c, d = self[1][0], self[1][1]
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return type(self)([[d, -b], [-c, a]])
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src = {}
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for r in range(height):
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for c in range(width):
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sign = -1 if (r + c) % 2 else 1
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src[r, c] = self.minor(r, c).determinant() * sign
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return type(self)(src, height, width)
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def inverse(self):
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if self.height == self.width == 1:
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return type(self)([[1. / self[0][0]]])
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return (1. / self.determinant()) * self.adjugate()
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def __add__(self, other):
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height, width = self.height, self.width
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if (height, width) != (other.height, other.width):
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raise ValueError('Must be same size')
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src = {}
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for r in range(height):
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for c in range(width):
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src[r, c] = self[r][c] + other[r][c]
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return type(self)(src, height, width)
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def __mul__(self, other):
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if self.width != other.height:
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raise ValueError('Bad size')
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height, width = self.height, other.width
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src = {}
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for r in range(height):
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for c in range(width):
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src[r, c] = sum(self[r][x] * other[x][c]
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for x in range(self.width))
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return type(self)(src, height, width)
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def __rmul__(self, other):
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if not isinstance(other, Number):
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raise TypeError('The operand should be a number')
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height, width = self.height, self.width
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src = {}
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for r in range(height):
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for c in range(width):
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src[r, c] = other * self[r][c]
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return type(self)(src, height, width)
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def __repr__(self):
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return '{}({})'.format(type(self).__name__, super(Matrix, self).__repr__())
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def _repr_latex_(self):
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rows = [' && '.join(['%.3f' % cell for cell in row]) for row in self]
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latex = r'\begin{matrix} %s \end{matrix}' % r'\\'.join(rows)
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return '$%s$' % latex
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def _gen_erfcinv(erfc, math=math):
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def erfcinv(y):
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"""The inverse function of erfc."""
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if y >= 2:
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return -100.
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elif y <= 0:
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return 100.
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zero_point = y < 1
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if not zero_point:
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y = 2 - y
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t = math.sqrt(-2 * math.log(y / 2.))
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x = -0.70711 * \
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((2.30753 + t * 0.27061) / (1. + t * (0.99229 + t * 0.04481)) - t)
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for i in range(2):
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err = erfc(x) - y
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x += err / (1.12837916709551257 * math.exp(-(x ** 2)) - x * err)
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return x if zero_point else -x
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return erfcinv
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def _gen_ppf(erfc, math=math):
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erfcinv = _gen_erfcinv(erfc, math)
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def ppf(x, mu=0, sigma=1):
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return mu - sigma * math.sqrt(2) * erfcinv(2 * x)
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return ppf
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def erfc(x):
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z = abs(x)
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t = 1. / (1. + z / 2.)
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r = t * math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (
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0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (
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0.27886807 + t * (-1.13520398 + t * (1.48851587 + t * (
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-0.82215223 + t * 0.17087277
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)))
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)))
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)))
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return 2. - r if x < 0 else r
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def cdf(x, mu=0, sigma=1):
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return 0.5 * erfc(-(x - mu) / (sigma * math.sqrt(2)))
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def pdf(x, mu=0, sigma=1):
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return (1 / math.sqrt(2 * math.pi) * abs(sigma) *
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math.exp(-(((x - mu) / abs(sigma)) ** 2 / 2)))
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ppf = _gen_ppf(erfc)
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def choose_backend(backend):
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if backend is None: # fallback
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return cdf, pdf, ppf
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elif backend == 'mpmath':
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try:
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import mpmath
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except ImportError:
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raise ImportError('Install "mpmath" to use this backend')
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return mpmath.ncdf, mpmath.npdf, _gen_ppf(mpmath.erfc, math=mpmath)
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elif backend == 'scipy':
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try:
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from scipy.stats import norm
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except ImportError:
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raise ImportError('Install "scipy" to use this backend')
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return norm.cdf, norm.pdf, norm.ppf
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raise ValueError('%r backend is not defined' % backend)
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def available_backends():
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backends = [None]
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for backend in ['mpmath', 'scipy']:
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try:
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__import__(backend)
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except ImportError:
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continue
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backends.append(backend)
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return backends
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class Node(object):
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pass
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class Variable(Node, Gaussian):
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def __init__(self):
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self.messages = {}
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super(Variable, self).__init__()
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def set(self, val):
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delta = self.delta(val)
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self.pi, self.tau = val.pi, val.tau
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return delta
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def delta(self, other):
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pi_delta = abs(self.pi - other.pi)
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if pi_delta == inf:
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return 0.
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return max(abs(self.tau - other.tau), math.sqrt(pi_delta))
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def update_message(self, factor, pi=0, tau=0, message=None):
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message = message or Gaussian(pi=pi, tau=tau)
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old_message, self[factor] = self[factor], message
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return self.set(self / old_message * message)
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def update_value(self, factor, pi=0, tau=0, value=None):
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value = value or Gaussian(pi=pi, tau=tau)
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old_message = self[factor]
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self[factor] = value * old_message / self
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return self.set(value)
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def __getitem__(self, factor):
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return self.messages[factor]
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def __setitem__(self, factor, message):
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self.messages[factor] = message
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def __repr__(self):
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args = (type(self).__name__, super(Variable, self).__repr__(),
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len(self.messages), '' if len(self.messages) == 1 else 's')
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return '<%s %s with %d connection%s>' % args
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class Factor(Node):
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def __init__(self, variables):
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self.vars = variables
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for var in variables:
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var[self] = Gaussian()
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def down(self):
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return 0
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def up(self):
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return 0
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@property
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def var(self):
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assert len(self.vars) == 1
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return self.vars[0]
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def __repr__(self):
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args = (type(self).__name__, len(self.vars),
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'' if len(self.vars) == 1 else 's')
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return '<%s with %d connection%s>' % args
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class PriorFactor(Factor):
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def __init__(self, var, val, dynamic=0):
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super(PriorFactor, self).__init__([var])
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self.val = val
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self.dynamic = dynamic
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def down(self):
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sigma = math.sqrt(self.val.sigma ** 2 + self.dynamic ** 2)
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value = Gaussian(self.val.mu, sigma)
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return self.var.update_value(self, value=value)
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class LikelihoodFactor(Factor):
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def __init__(self, mean_var, value_var, variance):
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super(LikelihoodFactor, self).__init__([mean_var, value_var])
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self.mean = mean_var
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self.value = value_var
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self.variance = variance
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def calc_a(self, var):
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return 1. / (1. + self.variance * var.pi)
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def down(self):
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# update value.
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msg = self.mean / self.mean[self]
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a = self.calc_a(msg)
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return self.value.update_message(self, a * msg.pi, a * msg.tau)
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def up(self):
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# update mean.
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msg = self.value / self.value[self]
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a = self.calc_a(msg)
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return self.mean.update_message(self, a * msg.pi, a * msg.tau)
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class SumFactor(Factor):
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def __init__(self, sum_var, term_vars, coeffs):
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super(SumFactor, self).__init__([sum_var] + term_vars)
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self.sum = sum_var
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self.terms = term_vars
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self.coeffs = coeffs
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def down(self):
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vals = self.terms
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msgs = [var[self] for var in vals]
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return self.update(self.sum, vals, msgs, self.coeffs)
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def up(self, index=0):
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coeff = self.coeffs[index]
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coeffs = []
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for x, c in enumerate(self.coeffs):
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try:
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if x == index:
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coeffs.append(1. / coeff)
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else:
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coeffs.append(-c / coeff)
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except ZeroDivisionError:
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coeffs.append(0.)
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vals = self.terms[:]
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vals[index] = self.sum
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msgs = [var[self] for var in vals]
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return self.update(self.terms[index], vals, msgs, coeffs)
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def update(self, var, vals, msgs, coeffs):
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pi_inv = 0
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mu = 0
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for val, msg, coeff in zip(vals, msgs, coeffs):
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div = val / msg
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mu += coeff * div.mu
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if pi_inv == inf:
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continue
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try:
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# numpy.float64 handles floating-point error by different way.
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# For example, it can just warn RuntimeWarning on n/0 problem
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# instead of throwing ZeroDivisionError. So div.pi, the
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# denominator has to be a built-in float.
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pi_inv += coeff ** 2 / float(div.pi)
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except ZeroDivisionError:
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pi_inv = inf
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pi = 1. / pi_inv
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tau = pi * mu
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return var.update_message(self, pi, tau)
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class TruncateFactor(Factor):
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def __init__(self, var, v_func, w_func, draw_margin):
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super(TruncateFactor, self).__init__([var])
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self.v_func = v_func
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self.w_func = w_func
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self.draw_margin = draw_margin
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def up(self):
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val = self.var
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msg = self.var[self]
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div = val / msg
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sqrt_pi = math.sqrt(div.pi)
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args = (div.tau / sqrt_pi, self.draw_margin * sqrt_pi)
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v = self.v_func(*args)
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w = self.w_func(*args)
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denom = (1. - w)
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pi, tau = div.pi / denom, (div.tau + sqrt_pi * v) / denom
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return val.update_value(self, pi, tau)
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#: Default initial mean of ratings.
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MU = 25.
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#: Default initial standard deviation of ratings.
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SIGMA = MU / 3
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#: Default distance that guarantees about 76% chance of winning.
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BETA = SIGMA / 2
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#: Default dynamic factor.
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TAU = SIGMA / 100
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#: Default draw probability of the game.
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DRAW_PROBABILITY = .10
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#: A basis to check reliability of the result.
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DELTA = 0.0001
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def calc_draw_probability(draw_margin, size, env=None):
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if env is None:
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env = global_env()
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return 2 * env.cdf(draw_margin / (math.sqrt(size) * env.beta)) - 1
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def calc_draw_margin(draw_probability, size, env=None):
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if env is None:
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env = global_env()
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return env.ppf((draw_probability + 1) / 2.) * math.sqrt(size) * env.beta
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|
|
|
|
|
def _team_sizes(rating_groups):
|
|
team_sizes = [0]
|
|
for group in rating_groups:
|
|
team_sizes.append(len(group) + team_sizes[-1])
|
|
del team_sizes[0]
|
|
return team_sizes
|
|
|
|
|
|
def _floating_point_error(env):
|
|
if env.backend == 'mpmath':
|
|
msg = 'Set "mpmath.mp.dps" to higher'
|
|
else:
|
|
msg = 'Cannot calculate correctly, set backend to "mpmath"'
|
|
return FloatingPointError(msg)
|
|
|
|
|
|
class Rating(Gaussian):
|
|
def __init__(self, mu=None, sigma=None):
|
|
if isinstance(mu, tuple):
|
|
mu, sigma = mu
|
|
elif isinstance(mu, Gaussian):
|
|
mu, sigma = mu.mu, mu.sigma
|
|
if mu is None:
|
|
mu = global_env().mu
|
|
if sigma is None:
|
|
sigma = global_env().sigma
|
|
super(Rating, self).__init__(mu, sigma)
|
|
|
|
def __int__(self):
|
|
return int(self.mu)
|
|
|
|
def __long__(self):
|
|
return long(self.mu)
|
|
|
|
def __float__(self):
|
|
return float(self.mu)
|
|
|
|
def __iter__(self):
|
|
return iter((self.mu, self.sigma))
|
|
|
|
def __repr__(self):
|
|
c = type(self)
|
|
args = ('.'.join([c.__module__, c.__name__]), self.mu, self.sigma)
|
|
return '%s(mu=%.3f, sigma=%.3f)' % args
|
|
|
|
|
|
class TrueSkill(object):
|
|
def __init__(self, mu=MU, sigma=SIGMA, beta=BETA, tau=TAU,
|
|
draw_probability=DRAW_PROBABILITY, backend=None):
|
|
self.mu = mu
|
|
self.sigma = sigma
|
|
self.beta = beta
|
|
self.tau = tau
|
|
self.draw_probability = draw_probability
|
|
self.backend = backend
|
|
if isinstance(backend, tuple):
|
|
self.cdf, self.pdf, self.ppf = backend
|
|
else:
|
|
self.cdf, self.pdf, self.ppf = choose_backend(backend)
|
|
|
|
def create_rating(self, mu=None, sigma=None):
|
|
if mu is None:
|
|
mu = self.mu
|
|
if sigma is None:
|
|
sigma = self.sigma
|
|
return Rating(mu, sigma)
|
|
|
|
def v_win(self, diff, draw_margin):
|
|
x = diff - draw_margin
|
|
denom = self.cdf(x)
|
|
return (self.pdf(x) / denom) if denom else -x
|
|
|
|
def v_draw(self, diff, draw_margin):
|
|
abs_diff = abs(diff)
|
|
a, b = draw_margin - abs_diff, -draw_margin - abs_diff
|
|
denom = self.cdf(a) - self.cdf(b)
|
|
numer = self.pdf(b) - self.pdf(a)
|
|
return ((numer / denom) if denom else a) * (-1 if diff < 0 else +1)
|
|
|
|
def w_win(self, diff, draw_margin):
|
|
x = diff - draw_margin
|
|
v = self.v_win(diff, draw_margin)
|
|
w = v * (v + x)
|
|
if 0 < w < 1:
|
|
return w
|
|
raise _floating_point_error(self)
|
|
|
|
def w_draw(self, diff, draw_margin):
|
|
abs_diff = abs(diff)
|
|
a, b = draw_margin - abs_diff, -draw_margin - abs_diff
|
|
denom = self.cdf(a) - self.cdf(b)
|
|
if not denom:
|
|
raise _floating_point_error(self)
|
|
v = self.v_draw(abs_diff, draw_margin)
|
|
return (v ** 2) + (a * self.pdf(a) - b * self.pdf(b)) / denom
|
|
|
|
def validate_rating_groups(self, rating_groups):
|
|
# check group sizes
|
|
if len(rating_groups) < 2:
|
|
raise ValueError('Need multiple rating groups')
|
|
elif not all(rating_groups):
|
|
raise ValueError('Each group must contain multiple ratings')
|
|
# check group types
|
|
group_types = set(map(type, rating_groups))
|
|
if len(group_types) != 1:
|
|
raise TypeError('All groups should be same type')
|
|
elif group_types.pop() is Rating:
|
|
raise TypeError('Rating cannot be a rating group')
|
|
# normalize rating_groups
|
|
if isinstance(rating_groups[0], dict):
|
|
dict_rating_groups = rating_groups
|
|
rating_groups = []
|
|
keys = []
|
|
for dict_rating_group in dict_rating_groups:
|
|
rating_group, key_group = [], []
|
|
for key, rating in iteritems(dict_rating_group):
|
|
rating_group.append(rating)
|
|
key_group.append(key)
|
|
rating_groups.append(tuple(rating_group))
|
|
keys.append(tuple(key_group))
|
|
else:
|
|
rating_groups = list(rating_groups)
|
|
keys = None
|
|
return rating_groups, keys
|
|
|
|
def validate_weights(self, weights, rating_groups, keys=None):
|
|
if weights is None:
|
|
weights = [(1,) * len(g) for g in rating_groups]
|
|
elif isinstance(weights, dict):
|
|
weights_dict, weights = weights, []
|
|
for x, group in enumerate(rating_groups):
|
|
w = []
|
|
weights.append(w)
|
|
for y, rating in enumerate(group):
|
|
if keys is not None:
|
|
y = keys[x][y]
|
|
w.append(weights_dict.get((x, y), 1))
|
|
return weights
|
|
|
|
def factor_graph_builders(self, rating_groups, ranks, weights):
|
|
flatten_ratings = sum(map(tuple, rating_groups), ())
|
|
flatten_weights = sum(map(tuple, weights), ())
|
|
size = len(flatten_ratings)
|
|
group_size = len(rating_groups)
|
|
# create variables
|
|
rating_vars = [Variable() for x in range(size)]
|
|
perf_vars = [Variable() for x in range(size)]
|
|
team_perf_vars = [Variable() for x in range(group_size)]
|
|
team_diff_vars = [Variable() for x in range(group_size - 1)]
|
|
team_sizes = _team_sizes(rating_groups)
|
|
# layer builders
|
|
def build_rating_layer():
|
|
for rating_var, rating in zip(rating_vars, flatten_ratings):
|
|
yield PriorFactor(rating_var, rating, self.tau)
|
|
def build_perf_layer():
|
|
for rating_var, perf_var in zip(rating_vars, perf_vars):
|
|
yield LikelihoodFactor(rating_var, perf_var, self.beta ** 2)
|
|
def build_team_perf_layer():
|
|
for team, team_perf_var in enumerate(team_perf_vars):
|
|
if team > 0:
|
|
start = team_sizes[team - 1]
|
|
else:
|
|
start = 0
|
|
end = team_sizes[team]
|
|
child_perf_vars = perf_vars[start:end]
|
|
coeffs = flatten_weights[start:end]
|
|
yield SumFactor(team_perf_var, child_perf_vars, coeffs)
|
|
def build_team_diff_layer():
|
|
for team, team_diff_var in enumerate(team_diff_vars):
|
|
yield SumFactor(team_diff_var,
|
|
team_perf_vars[team:team + 2], [+1, -1])
|
|
def build_trunc_layer():
|
|
for x, team_diff_var in enumerate(team_diff_vars):
|
|
if callable(self.draw_probability):
|
|
# dynamic draw probability
|
|
team_perf1, team_perf2 = team_perf_vars[x:x + 2]
|
|
args = (Rating(team_perf1), Rating(team_perf2), self)
|
|
draw_probability = self.draw_probability(*args)
|
|
else:
|
|
# static draw probability
|
|
draw_probability = self.draw_probability
|
|
size = sum(map(len, rating_groups[x:x + 2]))
|
|
draw_margin = calc_draw_margin(draw_probability, size, self)
|
|
if ranks[x] == ranks[x + 1]: # is a tie?
|
|
v_func, w_func = self.v_draw, self.w_draw
|
|
else:
|
|
v_func, w_func = self.v_win, self.w_win
|
|
yield TruncateFactor(team_diff_var,
|
|
v_func, w_func, draw_margin)
|
|
# build layers
|
|
return (build_rating_layer, build_perf_layer, build_team_perf_layer,
|
|
build_team_diff_layer, build_trunc_layer)
|
|
|
|
def run_schedule(self, build_rating_layer, build_perf_layer,
|
|
build_team_perf_layer, build_team_diff_layer,
|
|
build_trunc_layer, min_delta=DELTA):
|
|
if min_delta <= 0:
|
|
raise ValueError('min_delta must be greater than 0')
|
|
layers = []
|
|
def build(builders):
|
|
layers_built = [list(build()) for build in builders]
|
|
layers.extend(layers_built)
|
|
return layers_built
|
|
# gray arrows
|
|
layers_built = build([build_rating_layer,
|
|
build_perf_layer,
|
|
build_team_perf_layer])
|
|
rating_layer, perf_layer, team_perf_layer = layers_built
|
|
for f in chain(*layers_built):
|
|
f.down()
|
|
# arrow #1, #2, #3
|
|
team_diff_layer, trunc_layer = build([build_team_diff_layer,
|
|
build_trunc_layer])
|
|
team_diff_len = len(team_diff_layer)
|
|
for x in range(10):
|
|
if team_diff_len == 1:
|
|
# only two teams
|
|
team_diff_layer[0].down()
|
|
delta = trunc_layer[0].up()
|
|
else:
|
|
# multiple teams
|
|
delta = 0
|
|
for x in range(team_diff_len - 1):
|
|
team_diff_layer[x].down()
|
|
delta = max(delta, trunc_layer[x].up())
|
|
team_diff_layer[x].up(1) # up to right variable
|
|
for x in range(team_diff_len - 1, 0, -1):
|
|
team_diff_layer[x].down()
|
|
delta = max(delta, trunc_layer[x].up())
|
|
team_diff_layer[x].up(0) # up to left variable
|
|
# repeat until to small update
|
|
if delta <= min_delta:
|
|
break
|
|
# up both ends
|
|
team_diff_layer[0].up(0)
|
|
team_diff_layer[team_diff_len - 1].up(1)
|
|
# up the remainder of the black arrows
|
|
for f in team_perf_layer:
|
|
for x in range(len(f.vars) - 1):
|
|
f.up(x)
|
|
for f in perf_layer:
|
|
f.up()
|
|
return layers
|
|
|
|
def rate(self, rating_groups, ranks=None, weights=None, min_delta=DELTA):
|
|
rating_groups, keys = self.validate_rating_groups(rating_groups)
|
|
weights = self.validate_weights(weights, rating_groups, keys)
|
|
group_size = len(rating_groups)
|
|
if ranks is None:
|
|
ranks = range(group_size)
|
|
elif len(ranks) != group_size:
|
|
raise ValueError('Wrong ranks')
|
|
# sort rating groups by rank
|
|
by_rank = lambda x: x[1][1]
|
|
sorting = sorted(enumerate(zip(rating_groups, ranks, weights)),
|
|
key=by_rank)
|
|
sorted_rating_groups, sorted_ranks, sorted_weights = [], [], []
|
|
for x, (g, r, w) in sorting:
|
|
sorted_rating_groups.append(g)
|
|
sorted_ranks.append(r)
|
|
# make weights to be greater than 0
|
|
sorted_weights.append(max(min_delta, w_) for w_ in w)
|
|
# build factor graph
|
|
args = (sorted_rating_groups, sorted_ranks, sorted_weights)
|
|
builders = self.factor_graph_builders(*args)
|
|
args = builders + (min_delta,)
|
|
layers = self.run_schedule(*args)
|
|
# make result
|
|
rating_layer, team_sizes = layers[0], _team_sizes(sorted_rating_groups)
|
|
transformed_groups = []
|
|
for start, end in zip([0] + team_sizes[:-1], team_sizes):
|
|
group = []
|
|
for f in rating_layer[start:end]:
|
|
group.append(Rating(float(f.var.mu), float(f.var.sigma)))
|
|
transformed_groups.append(tuple(group))
|
|
by_hint = lambda x: x[0]
|
|
unsorting = sorted(zip((x for x, __ in sorting), transformed_groups),
|
|
key=by_hint)
|
|
if keys is None:
|
|
return [g for x, g in unsorting]
|
|
# restore the structure with input dictionary keys
|
|
return [dict(zip(keys[x], g)) for x, g in unsorting]
|
|
|
|
def quality(self, rating_groups, weights=None):
|
|
rating_groups, keys = self.validate_rating_groups(rating_groups)
|
|
weights = self.validate_weights(weights, rating_groups, keys)
|
|
flatten_ratings = sum(map(tuple, rating_groups), ())
|
|
flatten_weights = sum(map(tuple, weights), ())
|
|
length = len(flatten_ratings)
|
|
# a vector of all of the skill means
|
|
mean_matrix = Matrix([[r.mu] for r in flatten_ratings])
|
|
# a matrix whose diagonal values are the variances (sigma ** 2) of each
|
|
# of the players.
|
|
def variance_matrix(height, width):
|
|
variances = (r.sigma ** 2 for r in flatten_ratings)
|
|
for x, variance in enumerate(variances):
|
|
yield (x, x), variance
|
|
variance_matrix = Matrix(variance_matrix, length, length)
|
|
# the player-team assignment and comparison matrix
|
|
def rotated_a_matrix(set_height, set_width):
|
|
t = 0
|
|
for r, (cur, _next) in enumerate(zip(rating_groups[:-1],
|
|
rating_groups[1:])):
|
|
for x in range(t, t + len(cur)):
|
|
yield (r, x), flatten_weights[x]
|
|
t += 1
|
|
x += 1
|
|
for x in range(x, x + len(_next)):
|
|
yield (r, x), -flatten_weights[x]
|
|
set_height(r + 1)
|
|
set_width(x + 1)
|
|
rotated_a_matrix = Matrix(rotated_a_matrix)
|
|
a_matrix = rotated_a_matrix.transpose()
|
|
# match quality further derivation
|
|
_ata = (self.beta ** 2) * rotated_a_matrix * a_matrix
|
|
_atsa = rotated_a_matrix * variance_matrix * a_matrix
|
|
start = mean_matrix.transpose() * a_matrix
|
|
middle = _ata + _atsa
|
|
end = rotated_a_matrix * mean_matrix
|
|
# make result
|
|
e_arg = (-0.5 * start * middle.inverse() * end).determinant()
|
|
s_arg = _ata.determinant() / middle.determinant()
|
|
return math.exp(e_arg) * math.sqrt(s_arg)
|
|
|
|
def expose(self, rating):
|
|
k = self.mu / self.sigma
|
|
return rating.mu - k * rating.sigma
|
|
|
|
def make_as_global(self):
|
|
return setup(env=self)
|
|
|
|
def __repr__(self):
|
|
c = type(self)
|
|
if callable(self.draw_probability):
|
|
f = self.draw_probability
|
|
draw_probability = '.'.join([f.__module__, f.__name__])
|
|
else:
|
|
draw_probability = '%.1f%%' % (self.draw_probability * 100)
|
|
if self.backend is None:
|
|
backend = ''
|
|
elif isinstance(self.backend, tuple):
|
|
backend = ', backend=...'
|
|
else:
|
|
backend = ', backend=%r' % self.backend
|
|
args = ('.'.join([c.__module__, c.__name__]), self.mu, self.sigma,
|
|
self.beta, self.tau, draw_probability, backend)
|
|
return ('%s(mu=%.3f, sigma=%.3f, beta=%.3f, tau=%.3f, '
|
|
'draw_probability=%s%s)' % args)
|
|
|
|
|
|
def rate_1vs1(rating1, rating2, drawn=False, min_delta=DELTA, env=None):
|
|
if env is None:
|
|
env = global_env()
|
|
ranks = [0, 0 if drawn else 1]
|
|
teams = env.rate([(rating1,), (rating2,)], ranks, min_delta=min_delta)
|
|
return teams[0][0], teams[1][0]
|
|
|
|
|
|
def quality_1vs1(rating1, rating2, env=None):
|
|
if env is None:
|
|
env = global_env()
|
|
return env.quality([(rating1,), (rating2,)])
|
|
|
|
|
|
def global_env():
|
|
try:
|
|
global_env.__trueskill__
|
|
except AttributeError:
|
|
# setup the default environment
|
|
setup()
|
|
return global_env.__trueskill__
|
|
|
|
|
|
def setup(mu=MU, sigma=SIGMA, beta=BETA, tau=TAU,
|
|
draw_probability=DRAW_PROBABILITY, backend=None, env=None):
|
|
if env is None:
|
|
env = TrueSkill(mu, sigma, beta, tau, draw_probability, backend)
|
|
global_env.__trueskill__ = env
|
|
return env
|
|
|
|
|
|
def rate(rating_groups, ranks=None, weights=None, min_delta=DELTA):
|
|
return global_env().rate(rating_groups, ranks, weights, min_delta)
|
|
|
|
|
|
def quality(rating_groups, weights=None):
|
|
return global_env().quality(rating_groups, weights)
|
|
|
|
|
|
def expose(rating):
|
|
return global_env().expose(rating) |